Gist description...

wp-seo.php

add_action( 'init', 'jf_register_my_new_sitemap', 99 );
/**
 * On init, run the function that will register our new sitemap as well
 * as the function that will be used to generate the XML. This creates an
 * action that we can hook into built around the new 
 * sitemap name - 'wp_seo_do_sitemap_my_new_sitemap'
 */
function jf_register_my_new_sitemap() {
	global $wpseo_sitemaps;
	$wpseo_sitemaps->register_sitemap( 'my_new_sitemap', 'jf_generate_my_new_sitemap' );
}

add_action( 'wp_seo_do_sitemap_my_new_sitemap', 'jf_generate_my_new_sitemap' );
/**
 * Hook into this new action that we've built and output the XML associated with
 * what information we want to convey. Once the XML is built, set this as our sitemap
 * data
 */
function jf_generate_my_new_sitemap() {
	global $wpseo_sitemaps;

	//pull the required data, sort it as needed, build into $my_sitemap_data
	$my_sitemap_data = '<urlset xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:image="http://www.google.com/schemas/sitemap-image/1.1" xsi:schemaLocation="http://www.sitemaps.org/schemas/sitemap/0.9 http://www.sitemaps.org/schemas/sitemap/0.9/sitemap.xsd" xmlns="http://www.sitemaps.org/schemas/sitemap/0.9">
		<url>
			<loc>http://mydomain/</loc>
			<lastmod>2011-04-06T06:40:00+00:00</lastmod>
			<changefreq>weekly</changefreq>
			<priority>1</priority>
		</url>
		</urlset>';

	$wpseo_sitemaps->set_sitemap( $my_sitemap_data );
}

add_filter( 'wpseo_sitemap_index', 'jf_add_to_sitemap_index' );
/**
 * Filter the index page for the sitemaps (sitemap_index.xml) in order to
 * add our new sitemap.
 * 
 * @param $current_xml string representing the current index XML being shown
 *
 * @return string representing the new index XML to show
 */
function jf_add_to_sitemap_index( $current_xml ) {
	$current_xml .= '<sitemap>
		<loc>http://mynewdomain/my_new_sitemap-sitemap.xml</loc>
		<lastmod>2012-10-03T19:42:27+00:00</lastmod>
		</sitemap>';

	return $current_xml;
}

Thanks for this Jeremy, saved me a lot of time!

The line which calls add_action() isn't needed since register_sitemap() does it already.